R09 - December, 2011 - Regular Examinations - Set - 2.

B.Tech II Year - I Semester Examinations, December 2011
SIGNALS AND SYSTEMS
(COMMON TO ECE, EIE, BME, ETM, ICE)
Time: 3 hours Max. Marks: 75
Answer any five questions
All questions carry equal marks
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1.a) Define a complete set and hence show that the error can be minimized when the function f(t) is approximated using n set of orthogonal functions.
b) A rectangular function f(t) is defined by
Approximate this function by a waveform single term sint, two terms sint and sin3t, three terms sint, sin3t and sin5t over the interval (o, 2p) and show that the mean square error is minimum when the function is approximated by three terms rather than single term. [15]
2.a) Derive the necessary expression to represent the function f(t) using Trigonometric Fourier Series.
b) Bring out the relationship between Trigonometric and Exponential Fourier series. [15]
3.a) Prove that the time shift in time domain is equal to phase shift in frequency domain.
b) Find the Fourier transform of the function
i) f(t) = e-a|t| sin(t) ii) f(t) = cos at2 iii) f(t) = sin at2 [15]
4.a) What are the requirements to be satisfied by an LTI system to provide distortionless transmission of a signal?
b) Bring out the relation between bandwidth and rise time? [15]
5.a) Show that autocorrelation and power spectral density form a Fourier Transform Pair.
b) Discuss the process of extraction of a signal from noise in frequency domain. [15]
6. Define Sampling Theorem and discuss the way of performing sampling using impulse sampling technique. [15]
7.a) State and Prove Initial value and Final value theorem w.r.to Laplace transform.
b) Find the Laplace transform of the periodic rectangular wave shown in Figure.1. [15]
Figure.1
8.a) Determine the impulse and unit step response of the systems described by the difference equation y(n) = 0.6y(n-1)-0.08y(n-2) x(n)
b) Define Region of Convergence and state its properties w.r.to Z- Transform. [15]
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